Torus Calculator

V = 2π²Rr², SA = 4π²Rr.

How the Math Works

A torus is a doughnut-shaped surface formed by rotating a circle of radius r around an axis located at distance R from the circle's center. The volume is calculated using V = 2π²Rr², which squares the tube radius and multiplies by both radii and 2π squared. The surface area follows SA = 4π²Rr, representing the product of both radii multiplied by 4π squared. These formulas elegantly capture how the torus's size depends on both the thickness of the tube and the size of the hole in the center.

Practical Applications

Use this calculator when designing curved structures like arches, rings, or pipes in engineering and architecture. It's essential for determining material requirements in manufacturing items such as O-rings, gaskets, and decorative elements. The calculator helps verify if a curved design will fit within specified dimensions and provides precise measurements for fabrication, 3D printing, or construction projects requiring toroidal shapes.

Day-to-Day Use

Understanding torus calculations helps in everyday situations like determining how much resin or plastic is needed to 3D print a ring or decorative object. It's useful for DIY projects involving curved furniture joints, jewelry making, or crafting. Even when shopping for items like hula hoops or tires, knowing the volume helps estimate material quantity or compare product specifications, while surface area calculations assist in determining paint or coating requirements for circular objects.

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